There's a plugin like this on
http://techjoomla.com/documentation-for-invitex/invitex-easysocial-integration.html

Hello Andor,

I am sorry for the late reply.
I'm a little bit lost here, what do you mean by

Is it possible for a registered user to send an e-mail to a non-user requesting them to join?

Do you mean by sending invitation through emails to anyone inviting them to join EasySocial isn't? I believe the current system doesn't have this feature yet.

Hope this will help.
Thanks.